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Infinitesimal cohomology

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In mathematics, infinitesimal cohomology is a cohomology theory for algebraic varieties introduced by Grothendieck (1966). In characteristic 0 it is essentially the same as crystalline cohomology. In nonzero characteristic p Ogus (1975) showed that it is closely related to etale cohomology with mod p coefficients, a theory known to have undesirable properties.

References

  • Grothendieck, A. (1966), Letter to J. Tate (PDF)
  • Grothendieck, Alexander (1968), "Crystals and the de Rham cohomology of schemes", in Giraud, Jean; Grothendieck, Alexander; Kleiman, Steven L.; et al. (eds.), Dix Exposés sur la Cohomologie des Schémas (PDF), Advanced studies in pure mathematics, vol. 3, Amsterdam: North-Holland, pp. 306–358, MR 0269663 {{citation}}: Cite has empty unknown parameter: |1= (help)
  • Ogus, Arthur (1975), "Cohomology of the infinitesimal site.", Ann. Sci. École Norm. Sup. (4), 8 (3): 295–318, MR 0422280
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